Based on the assumption of weak dissipation introduced by Esposito et al. [Phys. Rev. Lett. 105, 150603 (2010)], analytic expressions for the efficiency bounds of several classes of typical thermodynamic cycles at the maximum power output are derived. The results obtained are of universal significance. They can be used to conveniently reveal the general characteristics of not only Carnot heat engines, but also isothermal chemical engines, non-Carnot heat engines, flux flow engines, gravitational engines, quantum Carnot heat engines, and two-level quantum Carnot engines at the maximum power output and to directly draw many important conclusions in the literature.

Here we report thermal evaporation dynamics of Au nanoparticles on single crystal oxide substrates, including MgO, SrTiO${}_3$, and Al${}_2$O${}_3$. The size reduction rate of Au nanoparticles via thermal treatments is strongly dependent on not only temperature but also pressure. Lowering the pressure of inert Ar gas from 10${}^5$ to 10 Pa increases the size reduction rate over 30 times in the temperature range 800 °C–950 °C. The temperature dependence is solely due to the variation of saturated vapor pressure of Au, whereas the pressure dependence of the surrounding inert gas can be interpreted in terms of a pressure dependence on a gas-phase diffusion of evaporated Au atoms into the surroundings. We present a simplified model to explain an evaporation dynamics, which well describes the pressure dependence on a size reduction rate of Au nanoparticles. By utilizing this useful pressure-induced evaporation dynamics, we succeeded in manipulating a size reduction of Au nanoparticle arrays down to −10 nm diameter range from −300 nm initial size by programming sequentially a surrounding pressure.

Modal relaxation dynamics has been observed experimentally to clarify statistical-physical properties of soft-mode turbulence, the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals. We found a dual structure, dynamical crossover associated with violation of time-reversal invariance, the corresponding time scales satisfying a dynamical scaling law. To specify the origin of the dual structure, the memory function due to nonthermal fluctuations has been defined by a projection-operator method and obtained numerically using experimental results. The results of the memory function suggest that the nonthermal fluctuations can be divided into Markov and non-Markov contributions; the latter is called the turbulent fluctuation (TF). Consequently, the relaxation dynamics is separated into three characteristic stages: bare-friction, early, and late stages. If the dissipation due to TFs dominates over that of the Markov contribution, the bare-friction stage contracts; the early and late stages then configure the dual structure. The memory effect due to TFs results in a time-reversible relaxation at the early stage, and the disappearance of the memory by turbulent mixing leads to a simple exponential relaxation at the late stage. Furthermore, the memory effect due to TFs is shown to originate from characteristic spatial coherency called the patch structure.

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport.

Stomata are pores responsible for gas exchange in leaves. Several experiments indicate that stomata synchronize into clusters or patches. The patches’ coordination may produce oscillations in stomatal conductance. Previous studies claim to reproduce some experimental results. However, none was able to explain the variety of behavior observed in the stomatal dynamics. Recently, Ferraz and Prado suggested a realistic geometry of vein distribution. Although it reproduces the patches, no oscillation was observed and the patches remain static. Without exploring significant details, the authors stated that hysteresis in stomatal aperture could explain several experimental features. In this paper, the hysteresis hypothesis is further explored through the concept of hysteretic operators. We have shown that the hysteresis assumption is sufficient to obtain dynamical patches and oscillations in stomatal conductance. The robustness of this hypothesis is tested by using different hysteresis operators. The model analysis reveals a dependence between the period of oscillation in stomatal conductance and the water deficit between the leaf and the environment. This underlying feature of the model might inspire further experiments to test this hypothesis.

Since mean-field approximations for susceptible-infected-susceptible (SIS) epidemics do not always predict the correct scaling of the epidemic threshold of the SIS metastable regime, we propose two novel approaches: (a) an $\varepsilon$-SIS generalized model and (b) a modified SIS model that prevents the epidemic from dying out (i.e., without the complicating absorbing SIS state). Both adaptations of the SIS model feature a precisely defined steady state (that corresponds to the SIS metastable state) and allow an exact analysis in the complete and star graph consisting of a central node and $N$ leaves. The $N$-intertwined mean-field approximation (NIMFA) is shown to be nearly exact for the complete graph but less accurate to predict the correct scaling of the epidemic threshold ${\tau }_c$ in the star graph, which is found as ${\tau }_c=\alpha {\tau }_c^{\left(1\right)}$, where $\alpha =\sqrt{\frac{1}{2}\log N+\frac{3}{2}\log \log N}$ and where ${\tau }_c^{\left(1\right)}=\frac{1}{\sqrt{N}}<{\tau }_c$ is the first-order epidemic threshold for the star in NIMFA and equal to the inverse of the spectral radius of the star's adjacency matrix.

A variant of the classic Saffman-Taylor instability problem is reported, in which the surface tension at the fluid-fluid interface depends on the interfacial curvature. We show that the interplay between the variable surface tension and three-dimensional effects connected to the contact angle significantly modifies the scenario of instability formation. This allows the manipulation of the Saffman-Taylor instability, leading to the stabilization (destabilization) of conventionally unstable (stable) situations. This is done analytically through a perturbative mode-coupling approach, providing relevant information about both linear and weakly nonlinear regimes of interface evolution.

A study is presented of the stochasticity in the orbit of a single, magnetized ion produced by the particle's interaction with two beating electrostatic waves whose frequencies differ by the ion cyclotron frequency. A second-order Lie transform perturbation theory is employed in conjunction with a numerical analysis of the maximum Lyapunov exponent to determine the velocity conditions under which stochasticity occurs in this dynamical system. Upper and lower bounds in ion velocity are found for stochastic orbits with the lower bound approximately equal to the phase velocity of the slower wave. A threshold condition for the onset of stochasticity that is linear with respect to the wave amplitudes is also derived. It is shown that the onset of stochasticity occurs for beating electrostatic waves at lower total wave energy densities than for the case of a single electrostatic wave or two nonbeating electrostatic waves.

By calculating correlation functions for the Lieb-Liniger model based on the algebraic Bethe ansatz method, we conduct a finite-size scaling analysis of the eigenstate thermalization hypothesis (ETH), which is considered to be a possible mechanism of thermalization in isolated quantum systems. We find that the ETH in a weak sense holds in the thermodynamic limit even for an integrable system, although it does not hold in the strong sense. Based on the result of the finite-size scaling analysis, we compare the contribution of the weak ETH to thermalization with that of yet another thermalization mechanism, the typicality, and show that the former gives only a logarithmic correction to the latter.

In this paper we assess the inherent uncertainty of one-dimensional diffusion processes via a stochasticity classification which provides an à la Mandelbrot categorization into five states of uncertainty: infra-mild, mild, borderline, wild, and ultra-wild. Two settings are considered. (i) Stopped diffusions: the diffusion initiates from a high level and is stopped once it first reaches a low level; in this setting we analyze the inherent uncertainty of the diffusion's maximal exceedance above its initial high level. (ii) Stationary diffusions: the diffusion is in dynamical statistical equilibrium; in this setting we analyze the inherent uncertainty of the diffusion's equilibrium level. In both settings general closed-form analytic results are established, and their application is exemplified by stock prices in the stopped-diffusions setting, and by interest rates in the stationary-diffusions setting. These results provide a highly implementable decision-making tool for the classification of uncertainty in the context of one-dimensional diffusions.

We study the dissipative quantum harmonic oscillator with general nonthermal preparations of the harmonic oscillator bath. The focus is on equilibration of the oscillator in the long-time limit and the additional requirements for thermalization. Our study is based on the exact solution of the microscopic model obtained by means of operator equations of motion, which provides us with the time evolution of the central oscillator density matrix in terms of the propagating function. We find a hierarchy of conditions for thermalization, together with the relation of the asymptotic temperature to the energy distribution in the initial bath state. We discuss the presence and absence of equilibration for the example of an inhomogeneous chain of harmonic oscillators, and we illustrate the general findings about thermalization for the nonthermal environment that results from a quench.

In this paper we study the role of noise in the context of resistive switching phenomena by means of experiments and numerical simulations. Experiments are conducted on a manganite sample. We show that the addition of external Gaussian noise to a small amplitude driving signal yields a contrast ratio between low- and high-resistance states, comparable to that obtained by the application of a large amplitude noiseless signal. Furthermore, excellent agreement between numerical simulation and measurement allows us to study resistive switching under varying input conditions and, thus, properly characterize the beneficial role of noise. We believe these results might be of relevance in the area of memory devices where the large scale of electronic integration renders the presence of noise unavoidable.

We investigate a nonequilibrium coarsening dynamics of a one-dimensional Ising spin system with chirality. Only spins at domain boundaries are updated so that the model undergoes a coarsening to either of equivalent absorbing states with all spins $+$ or $-$. Chirality is imposed by assigning different transition rates to events at down ($+-$) kinks and up ($-+$) kinks. The coarsening is characterized by power-law scalings of the kink density $\rho \sim t^{-\delta }$ and the characteristic length scale $\xi \sim t^{1/z}$ with time $t$. Surprisingly the scaling exponents vary continuously with model parameters, which is not the case for systems without chirality. These results are obtained from extensive Monte Carlo simulations and spectral analyses of the time evolution operator. Our study uncovers the novel universality class of the coarsening dynamics with chirality.

We present an experimental study of the deformation inside a granular material that is progressively tilted. We investigate the deformation before the avalanche with a spatially resolved diffusive wave spectroscopy setup. At the beginning of the inclination process, we first observe localized and isolated events in the bulk, with a density which decreases with the depth. As the angle of inclination increases, series of microfailures occur periodically in the bulk, and finally a granular avalanche takes place. The microfailures are observed only when the tilt angles are larger than a threshold angle much smaller than the granular avalanche angle. We have characterized the density of reorganizations and the localization of microfailures. We have also explored the effect of the nature of the grains, the relative humidity conditions, and the packing fraction of the sample. We discuss those observations in the framework of the plasticity of granular matter. Microfailures may then be viewed as the result of the accumulation of numerous plastic events.

Avoided level crossing muon spin resonance (ALC-$\mu$SR) spectroscopy was used to study radicals produced by the addition of the light hydrogen isotope muonium (Mu) to the discotic liquid crystal (DLC) 2,3,6,7,10,11-hexahexylthiotriphenylene (HHTT). Mu adds to the secondary carbon atoms of HHTT to produce a substituted cyclohexadienyl radical, whose identity was confirmed by comparing the measured hyperfine coupling constants with values obtained from DFT calculations. ALC-$\mu$SR spectra were obtained in the isotropic (I), hexagonal columnar (Col${}_{\mathrm{h}}$), helical (H), and crystalline (Cr) phases. In the I and Col${}_{\mathrm{h}}$ phases the radicals, which are incorporated within the stacks of HHTT molecules as isolated paramagnetic defects, undergo extremely rapid electron spin relaxation, on the order of a hundredfold faster than in the H or Cr phases. The electron spin relaxation rate increases significantly with increasing temperature and appears to be caused by the liquidlike motion within the columns, which modulates the overlap between the $\pi$ system of the radical and the $\pi$ systems of the neighboring HHTT molecules, and hence, the hyperfine coupling constants. Rapid electron spin relaxation should occur for any $\pi$ radical incorporated within the columns of a DLC, which may limit the utility of DLCs for future spin-based technologies.

Our work draws special attention to the importance of the effects of time-dependent parameters on decision making in bistable systems. Here, we extend previous studies of the mechanism known as speed-dependent cellular decision making in genetic circuits by performing an analytical treatment of the canonical supercritical pitchfork bifurcation problem with an additional time-dependent asymmetry and control parameter. This model has an analogous behavior to the genetic switch. In the presence of transient asymmetries and fluctuations, slow passage through the critical region in both systems increases substantially the probability of specific decision outcomes. We also study the relevance for attractor selection of reaching maximum values for the external asymmetry before and after the critical region. Overall, maximum asymmetries should be reached at an instant where the position of the critical point allows for compensation of the detrimental effects of noise in retaining memory of the transient asymmetries.

Stochasticity in ion channel gating is the major source of intrinsic neuronal noise, which can induce many important effects in neuronal dynamics. Several numerical implementations of the Langevin approach have been proposed to approximate the Markovian dynamics of the Hodgkin-Huxley neuronal model. In this work an improved channel-based Langevin approach is proposed by introducing a truncation procedure to limit the state fractions in the range of [0, 1]. The truncated fractions are put back into the state fractions in the next time step for channel noise calculation. Our simulations show that the bounded Langevin approaches combined with the restored process give better approximations to the statistics of action potentials with the Markovian method. As a result, in our approach the channel state fractions are disturbed by two terms of noise: an uncorrelated Gaussian noise and a time-correlated noise obtained from the truncated fractions. We suggest that the restoration of truncated fractions is a critical process for a bounded Langevin method.

Centipedes have many body segments and legs and they generate body undulations during terrestrial locomotion. Centipede locomotion has the characteristic that body undulations are absent at low speeds but appear at faster speeds; furthermore, their amplitude and wavelength increase with increasing speed. There are conflicting reports regarding whether the muscles along the body axis resist or support these body undulations and the underlying mechanisms responsible for the body undulations remain largely unclear. In the present study, we investigated centipede locomotion dynamics using computer simulation with a body-mechanical model and experiment with a centipede-like robot and then conducted dynamic analysis with a simple model to clarify the mechanism. The results reveal that body undulations in these models occur due to an instability caused by a supercritical Hopf bifurcation. We subsequently compared these results with data obtained using actual centipedes. The model and actual centipedes exhibit similar dynamic properties, despite centipedes being complex, nonlinear dynamic systems. Based on our findings, we propose a possible passive mechanism for body undulations in centipedes, similar to a follower force or jackknife instability. We also discuss the roles of the muscles along the body axis in generating body undulations in terms of our physical model.

Random threshold networks (RTNs) have been widely used as models of neural or genetic regulatory networks. Network topology plays a central role in the dynamics of these networks. Recently it has been shown that many social and biological networks are scale-free and also exhibit community structure, in which autonomous modules are wired together to perform relatively independent functions. In this study we use both synchronous and asynchronous models of RTNs to systematically investigate how community structure affects the dynamics of RTNs with scale-free topology. Extensive simulation experiments show that RTNs with high modularity have more attractors than those RTNs with low modularity, and RTNs with smaller communities tend to have more attractors. Damage resulting from perturbation of initial conditions spreads less effectively in RTNs with higher modularity and RTNs with smaller communities. In addition, RTNs with high modularity can coordinate their internal dynamics better than RTNs with low modularity under the synchronous update scheme, and it is the other way around under the asynchronous update. This study shows that community structure has a strong effect on the dynamics of RTNs.

The problem of sound propagation in a randomly inhomogeneous oceanic waveguide is considered. An underwater sound channel in the Sea of Japan is taken as an example. Our attention is concentrated on the domains of finite-range ray stability in phase space and their influence on wave dynamics. These domains can be found by means of the one-step Poincare map. To study manifestations of finite-range ray stability, we introduce the finite-range evolution operator (FREO) describing transformation of a wave field in the course of propagation along a finite segment of a waveguide. Carrying out statistical analysis of the FREO spectrum, we estimate the contribution of regular domains and explore their evanescence with increasing length of the segment. We utilize several methods of spectral analysis: analysis of eigenfunctions by expanding them over modes of the unperturbed waveguide, approximation of level-spacing statistics by means of the Berry-Robnik distribution, and the procedure used by A. Relano and coworkers [Relano et al., Phys. Rev. Lett. 89, 244102 (2002); Relano, Phys. Rev. Lett. 100, 224101 (2008)]. Comparing the results obtained with different methods, we find that the method based on the statistical analysis of FREO eigenfunctions is the most favorable for estimating the contribution of regular domains. It allows one to find directly the waveguide modes whose refraction is regular despite the random inhomogeneity. For example, it is found that near-axial sound propagation in the Sea of Japan preserves stability even over distances of hundreds of kilometers due to the presence of a shearless torus in the classical phase space. Increasing the acoustic wavelength degrades scattering, resulting in recovery of eigenfunction localization near periodic orbits of the one-step Poincaré map.